Research Article
Uniformly S-Noetherian rings
DOI:
10.2989/16073606.2023.2278744
Author(s):
Mingzhao ChenLeshan Normal University, China, Hwankoo KimHoseo University, Republic of Korea, Wei QiShandong University of Technology, China, Fanggui WangSichuan Normal University, China, Wei ZhaoABa Teachers University, China,
Keywords:
13E05, 13A15, 13C11, 13D30, Uniformly S-Noetherian ring, uniformly S-Noetherian module, u-S-injective module, trivial extension, pullback, amalgamated algebra,
Abstract
Let R be a ring and S be a multiplicative subset of R. Then R is called a uniformly S-Noetherian ring if there exists s ∈ S such that, for any ideal I of R, sI ⊆ K for some finitely generated subideal K of I. We give the Eakin-Nagata-Formanek theorem for uniformly S-Noetherian rings. In addition, the uniformly S-Noetherian properties on several ring constructions are given. The notion of u-S-injective modules is also introduced and studied. Finally, we obtain the Bass-Papp theorem for uniformly S-Noetherian rings.
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